Preheat oven to 350 degrees. Line a 13×9-inch pan with parchment paper. (Use a single piece across the pan to go up the sides and then tuck two smaller pieces under the sheet for the ends.)
In a medium bowl, combine 2 cups flour and powdered sugar. Cut butter into flour mix until it resembles coarse meal. Pat flour mixture into the bottom of the pan (it will seem a little dry) and bake for 25 to 30 minutes. Let the crust cool for at least 10 minutes before topping with filling.
In another bowl, combine eggs, sugar, 1/4 cup flour, lemon juice, lemon zest, and baking powder. Beat until blended and pour over cooked crust. Bake 25 minutes.
Allow to cool and sprinkle with powdered sugar. Remove from pan and cut into bars.